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Higher Algebra Hall & Knight Variation (Chapter 3) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 3 ‘Variation’ include stepwise solutions of the exercises that would help you in easy exam preparations. The chapter deals with the basics like inverse variation, joint variations and constants. The chapter also contains broad theoretical explanations and solved examples to help you assemble an enhanced understanding of direct variations, variation dependence, intermediate values, quantities that vary directly, jointly and inversely, and the concepts of work done. 

Chapter 3 ‘Variation’ of Higher Algebra By Hall and Knight has  1 exercise which has 22 questions.  Once you solve these questions you will learn to tackle problems related to volume, speed, distance and magnitude related to variations. All these questions will help you form a solid foundation for tough competitive exams like JEE, BITSAT and NEET. You can any time refer to our solutions for Higher Algebra By H.S. Hall and S.R. Knight and get a complete understanding of the concepts related to Variation. 

Instasolv’s solutions for Hall and Knight Higher Algebra Chapter 3 ‘Variation’ have been organized to ensure that you are not stuck in the chaos of looking for numerous resources. We aim at ensuring that all the important study material reaches to you from a single platform. Our subject experts have made sure that you get a productive, impactful and stress-free learning experience. We have ensured that all the solutions are based on the latest syllabus of Algebra for Class 12. 

Important Topics for  Higher Algebra by Hall and Knight Solutions Chapter 3: Variation

Direct Variation 

In this chapter, you will learn about direct variations. To understand this let us take an example of two quantities C and D. If these two quantities depend on each in such a manner that in case if we change the value of C, the value of D is also impacted and in case if we change the value of D, the value of C also undergoes a change in the same ratio, both the quantities are said to be in direct variation. 

This scenario can also be expressed as C is said to vary D (as it often occurs that the word director directly is omitted). This theory will be used in the chapter with respect to different scenarios like train speed, planet motion etc. Variation is expressed by the symbol – α. For example, the statement A varies B can also be expressed as A α B. 

Inverse Variation 

In this chapter, you will also learn about the concept of inverse variation which in simple words is a reverse concept of direct variation. Again taking the example of C and D, in case if the value of D undergoes a change, the value of C also changes but here if the value of D increases, the value of C will decrease and if the value of D decreases the value of C will increase. 

The same will occur in case of all the quantities that fall under inverse variation or vary inversely. Here you can even use one quantity to determine the other. For instance, in case if C = 4 when the value of D is 12

We can express it as 4 = m x 12

Therefore m = 1/3

C = 1/3 D 

m here is a constant value and will be used throughout the chapter to determine the values of the variables in the questions. 

Joint Variation

You will also learn about the concept of Joint Variation in this chapter. A quantity is said to vary jointly when the quantity varies directly with its product. For instance, A will be said to vary directly as B and inversely as C when A varies as B/C. 

In this scenario, the values happen to experience both inverse and direct variation simultaneously with one another. This concept is very important from the prospect of competitive exams and has also been used in the unsolved example questions. The chapter presents solved problems in order to develop a better understanding of Joint Variations and their importance in determining values and solving word problems. 

Exercise Discussions of Hall and Knight Higher Algebra Solutions Chapter 3: Variation

  • Hall & Knight Algebra Mathematics book with solutions for Variance contains answers to all 22 questions of the exercise. 
  • The exercise begins with a basic question where you are required to determine the values of the given variables according to the variation condition that has been given in the question statement.
  • The exercise contains questions which deal with inverse variations as well.
  • There are many condition-based questions which revolve around direct variations, square root values and cubes.
  • There are certain problems where you are required to determine and derive the relations between given terms on the basis of mentioned variations.
  • The exercise has word problems related to distance, volume, number of races and cost of a diamond
  • These questions also deal with time-related questions and numerical-based questions on the revolution of the moon and satellites. 

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